Add the following rational expressions. $\dfrac{6}{2x^2-7}+\dfrac{-3x-8}{2x^2-7}=$
Answer: We want to add two rational expressions whose denominators are equal. We can do this by adding the numerators and keeping the denominator the same. [Does this fit with how we add rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{6}{2x^2-7}+\dfrac{-3x-8}{2x^2-7} \\\\ &=\dfrac{(6)+(-3x-8)}{2x^2-7} \\\\ &=\dfrac{6-3x-8}{2x^2-7} \\\\ &=\dfrac{-3x-2}{2x^2-7} \end{aligned}$ In conclusion, $\dfrac{6}{2x^2-7}+\dfrac{-3x-8}{2x^2-7}=\dfrac{-3x-2}{2x^2-7}$